No, you’re not seeing things; this is a three-way homophone. Peak is most often used as a noun, referring to “a high point,” but it can also be used as a verb meaning “to reach a high point” or an adjective meaning “excellent.” Peek can be used as a noun meaning “a quick look” or as a verb meaning “to take a quick look.” Pique has multiple definitions as well, but I’ve heard it used most – if not exclusively – as a verb meaning “to arouse or stimulate.”

Examples:

Pikes Peak is named after the American explorer Zebulon Pike. We got tickets to a sneak peek of Tom Cruise’s latest movie. The new reality show looks horrible, but it has piqued some morbid curiosity of mine. The civil rights movement peaked in the 1960s.Peeking at another student’s paper during a test is cheating. If this doesn’t pique your interest, I don’t know what will. One must be in peak physical condition to run a marathon.